My understanding is that both the recipient can develop polio from OPV and also that the recipient can transmit the disease to others, it's just that the latter case (as you say) is the more common and much more worrying occurrence.
As my Dr said, the chances of the recipient developing polio from OPV are extremely low although she didn't state the reasons. I gather when it does happen usually there are mitigating circumstances - such as a weak immune system in combination with a vaccine whose viruses haven't been fully attenuated. Remember also that my OPV was a long while ago so these days we'd be working with updated information.
Although very rare, things can and do go wrong with vaccines - especially so during say a polio epidemic when everybody is in a panicky hurry. You've probably already read that in the 1950s during the early production of Salk's 'dead' IPV there were manufacturing problems where 'live' viruses had escaped into some finished vaccine batches and kids died as a result: https://www.washingtonpost.com/history/2020/04/14/cutter-pol....
This WP article on the polio epidemic and the botched vaccine provides an excellent summary of events and the sense of panic and fear people had (it describes events essentially as I recall them). At the time I was living in Australia but things were no different, we also had the disease and distance hadn't lessened our knowledge of kids dying from the vaccine in the US.
The article's quote that “…that polio was second only to the atomic bomb as the thing that Americans feared most,” would have equally applied in Australia. I recall the considerable anxiety and worry my parents had about the vaccine but everyone's fear of polio was much worse, so there was never any hesitation about us kids being immunized.
I'm unaware of the full extent of the political fallout from the US vaccine deaths but it's clear the tragedy delayed Australian kids from receiving the vaccine for about four to five years - for instance I didn't get immunized until I was in highschool (I think either in 1960 or '61).
This delay alone was a tragedy: for had it not happened then I'd be pretty certain that the kid in my primary school class who died of polio would not have done so. And that's just in my small world alone, similar tragic scenarios must have played out across the whole country.
It is interesting to muse about the public's overwhelmingly positive attitude to polio immunization in the '50s and '60s compared to the often hesitant and indifferent attitude of many with respect to the current COVID epidemic. Back then, despite their worries after the major tragedy of kids dying from a bad batch of vaccine, most people rationally weighed up the risk and rightly considered that being immunized with new fixed-up batches of vaccine was clearly the safest choice. It's a stark comparison with today where we have FUD and misinformation everywhere yet the newer vaccines are not only better but also much, much safer.
Undoubtedly, eventually some graduate student will do a PhD on the matter and we'll find out why a half century ago people were prepared to take sensible risks whereas today timidity and risk averseness reigns supreme.
Incidentally, another difference between the 1960s when I was vaccinated and now is that back then once the decision was eventually made to immunize kids it happened without any delay or mucking about. At my school, which was typical of other state schools, kids were vaccinated four classes at a time. Kids were lined up in the school's assembly hall in two rows of about 50 students - a line for boys and one for girls with both lines being vaccinated simultaneously - the same way recruits are vaccinated in the military. The operation commenced after the midmorning break and was complete by lunchtime - about 1,100 kids in total were processed in about two hours.